We consider a vertical cavity surface-emitting semiconductor laser whi
ch operates with two frequency-degenerate doughnut modes, and combinat
ions thereof. We identify a small region in the parameter space, where
there is bistability between the two doughnut states, and another dom
ain in which the TEM(10) mode, and all the configurations obtained fro
m it by rotation around the laser axis, are stable. The degeneracy by
rotation can be eliminated by considering a pump region of square sect
ion; in this case there is bistability between two stationary states,
in which the two intensity peaks are located along the diagonals of th
e square. In all the rest of the parameter space the system exhibits d
ynamical oscillations.